Question 856913
Tn = t * r^(n - 1)

T4 = t * r^(n - 1)
T5 = t * r^(n - 1)

T4+T5=144
 t * r^(3)+ t * r^(4)=144

T3 = t * r^(n - 1)
T2 = t * r^(n - 1)
T3+T2=16

 t * r+ t * r^2=16,
t * r^(3)+ t * r^(4)=144
r = 3,   t = 4/3
Your question is poorly worded. 
Do you want just the 6th term or the sum of the first six terms?
r = 3,   t = 4/3
Tn = t * r^(n - 1)
T6 = 4/3 * 3^(5)=324
The sixth term is 324

S=t*(1 - r^n)/(1 - r)
S=4/3*(1 - 3^6)/(1 -  3)

S=1456/3 
S=485 1/3
The sum of the first six terms is 485 1/3